Nuprl Lemma : ohc_v1_strict_inc_rounds
es:EO'. e1,e2:E. Cmd:ValueAllType. n,round1,round2:
.
((
z: 
Cmd
round:
e:E
(e1 
loc e
(e <loc e2)
z 
ohc_v1_RoundInfo(Cmd)(e)
round ohc_v1_NewRoundsState(Cmd) n(e)
let z,c = z
in let m,i = z
in (round < i) (n = m)))
(e1 <loc e2)
round1 ohc_v1_NewRoundsState(Cmd) n(e1)
round2 ohc_v1_NewRoundsState(Cmd) n(e2)
(round1 < round2))
Proof not projected
Definitions occuring in Statement :
ohc_v1_NewRoundsState: ohc_v1_NewRoundsState(Cmd),
ohc_v1_RoundInfo: ohc_v1_RoundInfo(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-E: E,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
less_than: a < b,
apply: f a,
spread: spread def,
product: x:A B[x],
int: ,
equal: s = t,
vatype: ValueAllType
Definitions :
all: x:A. B[x],
vatype: ValueAllType,
implies: P Q,
exists: x:A. B[x],
and: P Q,
ohc_v1_RoundInfo: ohc_v1_RoundInfo(Cmd),
ohc_v1_update_round: ohc_v1_update_round(Cmd),
ohc_v1_init: ohc_v1_init(),
prop: 
,
trans: Trans(T;x,y.E[x; y]),
not: 
A,
member: t T,
so_lambda: 
x.t[x],
cand: A c B,
ifthenelse: if b then t else f fi ,
band: p 
q,
btrue: tt,
uiff: uiff(P;Q),
assert: 
b,
guard: {T},
bfalse: ff,
squash: 
T,
true: True,
false: False,
ohc_v1_retry'base: ohc_v1_retry'base(Cmd),
ohc_v1_prop2retry: ohc_v1_prop2retry(Cmd),
ohc_v1_proposal'base: ohc_v1_proposal'base(Cmd),
name: Name,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
atom-deq: AtomDeq,
eq_atom: x =a y,
ohc_v1_NewRoundsState: ohc_v1_NewRoundsState(Cmd),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
bool: 
,
unit: Unit,
uimplies: b supposing a,
or: P 
Q,
iff: P 
Q,
sq_type: SQType(T),
so_apply: x[s],
it: 
,
subtype: S 
T
Lemmas :
Memory-class-progress,
and_wf,
less_than_wf,
equal_wf,
ohc_v1_update_round_wf,
ohc_v1_init_wf,
Id_wf,
bag_wf,
ohc_v1_RoundInfo_wf,
decidable__cand,
decidable__lt,
decidable__equal_int,
sq_stable_from_decidable,
band_wf,
eq_int_wf,
lt_int_wf,
bool_wf,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_band,
and_functionality_wrt_uiff,
assert_of_eq_int,
assert_of_lt_int,
iff_transitivity,
bor_wf,
bnot_wf,
le_int_wf,
or_wf,
not_wf,
le_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_thru_band,
squash_wf,
true_wf,
bnot_of_lt_int,
assert_of_bor,
or_functionality_wrt_uiff,
assert_of_bnot,
not_functionality_wrt_uiff,
assert_of_le_int,
not_over_and,
subtype_base_sq,
int_subtype_base,
classrel_wf,
Memory-class_wf,
es-locl_wf,
event-ordering+_inc,
Message_wf,
es-le_wf,
parallel-class-single-val,
ohc_v1_retry'base_wf,
simple-loc-comb-1_wf,
concat-lifting-loc-1_wf,
ohc_v1_prop2retry_wf,
ohc_v1_proposal'base_wf,
disjoint-classrel-symm,
simple-loc-comb-1-concat-disjoint-classrel,
base-disjoint-classrel,
assert-name_eq,
name_wf,
simple-loc-comb-1-concat-single-val,
single-valued-classrel-base,
single-valued-bag-single,
es-E_wf,
exists_wf,
ohc_v1_NewRoundsState_wf,
valueall-type_wf,
event-ordering+_wf
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}n,round1,round2:\mBbbZ{}.
((\mexists{}z:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd
\mexists{}round:\mBbbZ{}
\mexists{}e:E
(e1 \mleq{}loc e
\mwedge{} (e <loc e2)
\mwedge{} z \mmember{} ohc\_v1\_RoundInfo(Cmd)(e)
\mwedge{} round \mmember{} ohc\_v1\_NewRoundsState(Cmd) n(e)
\mwedge{} let z,c = z
in let m,i = z
in (round < i) \mwedge{} (n = m)))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} round1 \mmember{} ohc\_v1\_NewRoundsState(Cmd) n(e1)
{}\mRightarrow{} round2 \mmember{} ohc\_v1\_NewRoundsState(Cmd) n(e2)
{}\mRightarrow{} (round1 < round2))
Date html generated:
2012_02_20-PM-05_25_43
Last ObjectModification:
2012_02_13-PM-01_04_11
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